DISCUSIÓN DE RESULTADOS

Groundwater flow in aquifers is often simulated under the assumptions that the density is constant and that the principal components of the hydraulic conductivity tensor are aligned with coordinate axes of

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the model grid so that all of the nonprincipal components equal zero. Under these assumptions, the groundwater flow partial- differential equation is (McDonald and Harbaugh,1988): t h s S s q i x h i K i x ∂ ∂ = + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ∂ ∂ ∂ ∂ (6-1)

where Ki = the principal component of the hydraulic conductivity tensor, (LT-1); h = the potentiometric head (L);

qS = the volumetric flux per unit volume representing sources and/or sinks of water, with qS <0.0 for flow out of the groundwater system and qS >0.0 for flow into the

groundwater system (T-1); SS = the specific storage of the porous material (L-1); and t = time (T). It is assumed that the Einstein summation convention applies in Equation 6-1.

The groundwater flow equation is usually solved numerically by finite differences or by finite elements. The flow region is subdivided into blocks in which the medium properties are assumed to be uniform. A flow equation is written for each block, called a cell. Thus the geometry of each cell must be specified as well as the hydraulic conductivity and net flux of water to or from the cell must be specified. In some

instances, the groundwater head for a cell can be specified.

The first step in formulating the conceptual model is to define the physical area of interest, i.e., to identify the boundaries of the model. In addition to defining the model boundaries, the boundaries of each hydrogeologic unit must be defined. In general each hydrogeologic unit is a connected region having the same mean hydraulic conductivity. In some cases, the hydraulic conductivity in all model cells inside a hydrogeologic unit are set equal to the mean value. In other cases, the

hydraulic conductivity within the

hydrogeologic unit may be assumed to be spatially variable, in which case the

hydraulic conductivity may be geostatistically generated.

Numerical models for the groundwater flow system require boundary conditions, such that the head or flux is specified along the boundaries of the system (Anderson and Woessner, 1992). Whenever possible, the boundary conditions should coincide with natural hydrogeologic boundaries such as topographic divides, in which case the natural boundary condition is a constant head boundary condition. Alternatively, an impermeable strata present in the system can be natural hydrogeologic boundaries; in this instance the no flow boundary condition is appropriate.

Several kinds of fluid sources and sinks including flow to and from wells, recharge, evapotranspiration, rivers, streams, constant- head boundaries, drains, and lakes may need to be considered in formulating the flow model. Even though the locations of these fluid sources may not correspond to the model boundaries, each can be considered a boundary condition in that fluid either enters or leaves the model domain, even when the fluid source is located inside the model boundaries. In general, these boundary conditions can be classified as either prescribed flux boundary conditions or as head-dependent boundary conditions. Prescribed flux boundary conditions are used, for example, in the case of a pumped well or to represent recharge to an aquifer or discharge from a spring. Head-dependent boundary conditions are commonly used in rivers and streams where the direction of groundwater flow may be either to or from the aquifer, with the flux controlled by the difference in head and the conductance of the river bed.

A transient groundwater flow model is needed in cases where the boundary conditions vary with time, e.g. dynamic fluid sources or constant head nodes that change with time. In such cases, it may be possible to assume that the flow system can be described as a series of steady state

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models where the boundary conditions change abruptly at the beginning of each period. In more complex scenarios, fully transient simulations can be obtained by specifying the temporal behavior of the boundary conditions.

Groundwater flow models are typically calibrated in a stepwise and iterative manner where the hydraulic conductivity and boundary conditions are progressively refined and model complexity is gradually increased to optimize the match to

calibration data (Hill, 1998, 2006). Traditionally, calibration data consisted of hydraulic heads and the primary variable obtained by model calibration by an ad hoc adjustment to the hydraulic conductivity. Hydraulic conductivity values can be estimated independently of the flow model by conducting field tests such as pump or slug tests. However, even when these variables are estimated independently, model calibration may be necessary to improve model fit. More recently it has been recognized that flow model calibration can be improved by including groundwater flux estimates such as discharge to springs in the calibration data set (D’Agnese et al., 1999). Including these flows in the calibration data is particularly important in steady state models because in many such instances simulated heads are insensitive to aquifer properties such as hydraulic conductivity. Software for conducting groundwater model calibration analyses are now readily

available (Doherty 2004; Poeter et al., 2005) and guidelines for applying these tools have also been presented (Hill, 1998). These tools provide efficient means for conducting the necessary nonlinear regression analyses and also provide sensitivity analysis results. The sensitivity analyses help identify which data and which parameters are contributing most significantly to the model fit.

Monitoring these results can suggest when to add additional data or parameters (processes) to the model calibration effort.

Model complexity is increased gradually in order to account for significant features in the observations while maintaining the principle of parsimony. However, it has been noted that determining the appropriate level of model complexity is an ill defined process (Hill, 2006).

Equation 6-1, when combined with boundary and initial conditions, describes transient three-dimensional ground-water flow in a heterogeneous and anisotropic medium, provided that the principal axes of hydraulic conductivity are aligned with the coordinate directions. Solution of this equation gives the groundwater head and water fluxes for each of the fluid sources but the solution does not directly yield

groundwater velocities.